A Unique QP Partitioning and Siegert Width Using Real-Valued Continuum-Remover Potential

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A simple, practical quantum chemical procedure is presented for computing the energy position and the decay width of autoionization resonances. It combines the L²-stabilized resonance wave function obtained using the real-valued continuum-remover (CR) potential [Y. Sajeev Chem. Phys. Lett.2013, 587, 105–112] and the Feshbach projection operator (FPO) partitioning technique. Unlike the conventional FPO partitioning of the total wave function into its resonant space and background space components, an explicit partitioning of the total wave function into its interaction region and noninteraction region components is obtained with the help of real-valued continuum-remover potential. The molecular system is initially confined inside a CR potential which removes the electronic continuum of the molecular system in which its resonance state is embedded and, thus, unravels the space component of the resonance wave function as a bound, localized eigenstate of the confined system. The eigenfunctions of the molecular Hamiltonian represented in the space constitute a complementary, orthogonal space. A unique partition is obtained when the level-shift of the space function due to its coupling with the space is zero, and the resonance width is computed using these unique partitioned spaces. This new procedure, which we refer to as CR-FPO formalism, is formally very simple and straightforward to implement, yet its applications to the resonance state of a model Hamiltonian and to the doubly excited resonance states of atomic and molecular systems at the full-CI level are very accurate as compared to the alternative, very precise L² methods. In addition, the CR-FPO formalism is implemented in the multireference configuration interaction (MRCI) method, and uses it for calculating the energy position and the autionization decay width of ²Π_g shape resonance in N₂^–.